Question

lf 3x-4y=10 and xy=-1,find the value of 9x2+16y2
with full explaination
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Answer 1

( 3x - 4y ) = 10



$\bold{Square \: \: on \: \: both \: \: sides, }$


=> ( 3x - 4y )² = 10²



$\bold{We \: \: know, \: \: ( a - b ) ^{2} = a^{2} + b^{2} - 2ab}$


=> ( 3x )² + ( 4y )² - 2( 3x × 4y ) = 100


=> 9x² + 16y - 24( xy ) = 100

=> 9x² + 16y² - 24( - 1 ) = 100

=> 9x² + 16y² + 24 = 100

=> 9x² + 16y² = 100 - 24


=> 9x² + 16y² = 76

Answer 2

Given Equation is 3x - 4y = 10 ------ (1)

Given Equation is xy = -1 ------ (2)

On squaring equation (1) on both sides, we get

= > (3x - 4y)^2 = (10)^2

= > (3x)^2 + (4y)^2 - 2(3x)(4y)= 100

= > 9x^2 + 16y^2 - 24(xy) = 100

= > 9x^2 + 16y^2 - 24(-1) = 100

= > 9x^2 + 16y^2 + 24 = 100

= > 9x^2 + 16y^2 = 100 - 24

= > 9x^2 + 16y^2 = 76.

Hope this helps!